1 Preferred Experiment

Original Pref Length = 9600 Filtered Pref Length = 9478

Original Smallt Length = 9600 Filtered Smallt Length = 9453

Original Pilot Length = 13994 Filtered Pilot Length = 13994

1.1 Across prefs

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.

1.2 Movement Duration

Table 1.1: Movement duration linear models.
Duration Linear Estimate P-Value Std Error
Circle 3.196e-02 0.000e+00 1.022e-03
Pilot 3.830e-02 0.000e+00 8.766e-04
Arc 3.376e-02 0.000e+00 9.952e-04
All 3.518e-02 0.000e+00 5.549e-04
Table 1.1: Movement duration average values, NO propogated error ALL AVG (s)
Effective Mass (kg) 2a 2b 2c
2.5 0.781±0.047 0.846±0.043 0.667±0.057
3.8 0.844±0.05 0.902±0.043 0.743±0.061
4.7 0.868±0.049 0.926±0.046 0.782±0.067
6.1 0.904±0.051 0.973±0.043 0.823±0.073
Table 1.1: Movement duration average values (s). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 0.7804±0.0798 0.8456±0.0869 0.6674±0.1233
3.8 0.8432±0.0981 0.9020±0.1021 0.7428±0.1204
4.7 0.8669±0.1082 0.9268±0.0982 0.7814±0.1593
6.1 0.9039±0.1120 0.9733±0.1128 0.8228±0.1803
Table 1.1: Movement duration average values with PROPGATED ERROR (s)
Effective Mass (kg) 2a 2b 2c
2.5 0.7804±0.0413 0.8456±0.0239 0.6674±0.0157
3.8 0.8432±0.0419 0.9020±0.0225 0.7428±0.0180
4.7 0.8669±0.0387 0.9268±0.0245 0.7814±0.0175
6.1 0.9039±0.0404 0.9733±0.0216 0.8228±0.0182

There is an overall effect of mass on movement duration (slope = 3.199e-02, p = 0.000e+00).

Experiment 2b movement duration is not different from 2a (p = 2.590e-01).

Experiment 2c movement duration is significantly lower than 2a (slope = -1.301e-01, p = 1.723e-03).

The interesting thing with these are the interaction effects.

Experiment 2b movement duration increases with mass more than experiment 2a (slope = 1.770e-03, p = 2.257e-01).

Experiment 2c movement duration increases with mass more than experiment 2a (slope = 6.323e-03, p = 2.284e-06).

Movement Duration by experiment.

Figure 1.1: Movement Duration by experiment.

1.2.1 Movement Duration Norm

Table 1.2: Movement duration linear models.
Duration Linear Estimate P-Value Std Error
Circle 4.152e-02 0.000e+00 1.304e-03
Pilot 5.797e-02 0.000e+00 1.313e-03
Arc 3.986e-02 0.000e+00 1.166e-03
All 4.803e-02 0.000e+00 7.529e-04
Table 1.2: Movement duration average values, NO propogated error ALL AVG (s)
Effective Mass (kg) 2a 2b 2c
2.5 1±0.052 1±0.045 1±0.064
3.8 1.085±0.062 1.067±0.043 1.124±0.086
4.7 1.112±0.054 1.096±0.047 1.175±0.081
6.1 1.162±0.06 1.15±0.042 1.234±0.083
Table 1.2: Movement duration NORM average values (s). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 1.0000±0.0000 1.0000±0.0000 1.0000±0.0000
3.8 1.0849±0.1255 1.0666±0.0380 1.1238±0.1227
4.7 1.1115±0.0855 1.0963±0.0370 1.1749±0.1368
6.1 1.1614±0.1187 1.1503±0.0496 1.2338±0.1409
Table 1.2: Movement duration NORM average values with PROPGATED ERROR (s)
Effective Mass (kg) 2a 2b 2c
2.5 1.0000±0.0519 1.0000±0.0279 1.0000±0.0227
3.8 1.0849±0.0521 1.0666±0.0256 1.1238±0.0277
4.7 1.1115±0.0486 1.0963±0.0287 1.1749±0.0252
6.1 1.1614±0.0507 1.1503±0.0251 1.2338±0.0256

There is an overall effect of mass on movement duration (slope = 4.157e-02, p = 0.000e+00).

Experiment 2b movement duration is not different from 2a (p = 7.798e-01).

Experiment 2c movement duration is not different from 2a (p = 1.485e-01).

The interesting thing with these are the interaction effects.

Experiment 2b movement duration did NOT change with mass more than 2a. (p = 3.898e-01).

Experiment 2c movement duration increases with mass more than experiment 2a (slope = 1.641e-02, p = 0.000e+00).

Movement Duration by experiment.

(#fig:movedur_normbyexperiment)Movement Duration by experiment.

1.3 Peak Velocity

Table 1.3: Peak Velocity linear models.
Velocity Linear Estimate P-Value Std Error
Circle -1.300e-02 0.000e+00 2.736e-04
Pilot -1.990e-02 0.000e+00 3.156e-04
Arc -1.130e-02 0.000e+00 2.106e-04
All -1.544e-02 0.000e+00 1.692e-04
Table 1.3: Peak Velocity average values, NO propogated error ALL AVG (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 0.261±0.075 0.227±0.066 0.391±0.092
3.8 0.232±0.067 0.206±0.059 0.345±0.081
4.7 0.222±0.064 0.199±0.058 0.335±0.079
6.1 0.211±0.061 0.184±0.053 0.314±0.074
Table 1.3: Peak Velocity average values (m/s). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 0.2610±0.0387 0.2274±0.0391 0.3913±0.1043
3.8 0.2322±0.0422 0.2059±0.0345 0.3451±0.0735
4.7 0.2228±0.0381 0.1991±0.0357 0.3350±0.0888
6.1 0.2113±0.0378 0.1838±0.0365 0.3136±0.0822
Table 1.3: Peak Velocity average values with PROPGATED ERROR (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 0.2610±0.0112 0.2274±0.0045 0.3913±0.0051
3.8 0.2322±0.0103 0.2059±0.0044 0.3451±0.0045
4.7 0.2228±0.0092 0.1991±0.0043 0.3350±0.0046
6.1 0.2113±0.0090 0.1838±0.0038 0.3136±0.0041

There is an overall effect of mass on peak velocity (slope = -1.300e-02, p = 0.000e+00).

Experiment 2b peak velocity is not different from 2a (p = 1.599e-01).

Experiment 2c peak velocity is significantly greater than 2a (slope = 1.453e-01, p = 2.233e-10).

The interesting thing with these are the interaction effects.

Experiment 2b peak velocity increases with mass more than experiment 2a (slope = 1.690e-03, p = 1.321e-04).

Experiment 2c peak velocity decreases with mass more than experiment 2a (slope = -6.910e-03, p = 0.000e+00).

Peak Velocity by experiment.

Figure 1.2: Peak Velocity by experiment.

1.3.1 Peak Velocity Normalized

## boundary (singular) fit: see help('isSingular')
Table 1.4: Peak Velocity linear models.
Velocity Linear Estimate P-Value Std Error
Circle -4.881e-02 0.000e+00 1.027e-03
Pilot -5.037e-02 0.000e+00 7.768e-04
Arc -5.022e-02 0.000e+00 9.117e-04
All -4.987e-02 0.000e+00 5.215e-04
Table 1.4: Peak Velocity average values, NO propogated error ALL AVG (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 1±0.289 1±0.289 1±0.236
3.8 0.895±0.258 0.906±0.262 0.897±0.211
4.7 0.855±0.247 0.876±0.253 0.86±0.203
6.1 0.814±0.235 0.806±0.233 0.805±0.19
Table 1.4: Peak Velocity NORM average values (m/s). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 1.0000±0.0000 1.0000±0.0000 1.0000±0.0000
3.8 0.8950±0.1284 0.9063±0.0448 0.8967±0.0993
4.7 0.8553±0.1025 0.8756±0.0523 0.8603±0.0941
6.1 0.8145±0.1288 0.8061±0.0475 0.8049±0.0938
Table 1.4: Peak Velocity NORM average values with PROPGATED ERROR (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 1.0000±0.0428 1.0000±0.0197 1.0000±0.0127
3.8 0.8950±0.0393 0.9063±0.0191 0.8967±0.0119
4.7 0.8553±0.0350 0.8756±0.0186 0.8603±0.0120
6.1 0.8145±0.0351 0.8061±0.0165 0.8049±0.0106

There is an overall effect of mass on peak velocity (slope = -4.876e-02, p = 0.000e+00).

Experiment 2b peak velocity is not different from 2a (p = 6.286e-01).

Experiment 2c peak velocity is not different from 2a (p = 7.392e-01).

The interesting thing with these are the interaction effects.

Experiment 2b peak velocity did NOT change with mass more than 2a. (p = 2.847e-01).

Experiment 2c peak velocity did NOT change with mass more than 2a. (p = 1.907e-01).

Peak Velocity by experiment.

Figure 1.3: Peak Velocity by experiment.

1.4 Reaction Time

Table 1.5: Reaction Time linear models.
Reaction Time Linear Estimate P-Value Std Error
Circle 4.882e-03 0.000e+00 4.768e-04
Pilot 5.688e-03 0.000e+00 4.167e-04
Arc 6.182e-03 0.000e+00 4.260e-04
All 5.607e-03 0.000e+00 2.556e-04
Table 1.5: Reaction time average values, NO propogated error ALL AVG (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 0.184±0.015 0.208±0.018 0.201±0.014
3.8 0.194±0.024 0.217±0.018 0.214±0.02
4.7 0.198±0.019 0.22±0.017 0.219±0.016
6.1 0.203±0.02 0.232±0.018 0.223±0.02
Table 1.5: Reaction time average values (s). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 0.1839±0.0231 0.2075±0.0214 0.2011±0.0223
3.8 0.1939±0.0281 0.2171±0.0180 0.2141±0.0357
4.7 0.1979±0.0302 0.2199±0.0143 0.2186±0.0327
6.1 0.2024±0.0315 0.2317±0.0227 0.2230±0.0359
Table 1.5: Reaction time average values with PROPGATED ERROR (s)
Effective Mass (kg) 2a 2b 2c
2.5 0.1839±0.0140 0.2075±0.0084 0.2011±0.0054
3.8 0.1939±0.0231 0.2171±0.0084 0.2141±0.0076
4.7 0.1979±0.0176 0.2199±0.0085 0.2186±0.0062
6.1 0.2024±0.0179 0.2317±0.0085 0.2230±0.0078

There is an overall effect of mass on reaction_time (slope = 4.923e-03, p = 0.000e+00).

Experiment 2b reaction_time is not different from 2a (p = 9.261e-02).

Experiment 2c reaction_time is not different from 2a (p = 1.129e-01).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_time did NOT change with mass more than 2a. (p = 6.315e-02).

Experiment 2c reaction_time did NOT change with mass more than 2a. (p = 2.144e-01).

Reaction Time by experiment.

Figure 1.4: Reaction Time by experiment.

1.4.1 Reaction Time Normalized

## boundary (singular) fit: see help('isSingular')
Table 1.6: Reaction Time linear models.
Reaction Time Norm Linear Estimate P-Value Std Error
Circle 2.584e-02 0.000e+00 2.428e-03
Pilot 2.774e-02 0.000e+00 1.935e-03
Arc 3.037e-02 0.000e+00 2.076e-03
All 2.800e-02 0.000e+00 1.235e-03
Table 1.6: Reaction time average values, NO propogated error ALL AVG (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 1±0.075 1±0.081 1±0.062
3.8 1.055±0.118 1.049±0.082 1.062±0.082
4.7 1.074±0.092 1.064±0.084 1.085±0.072
6.1 1.099±0.092 1.118±0.085 1.107±0.086
Table 1.6: Reaction time NORM average values (s). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 1.0000±0.0000 1.0000±0.0000 1.0000±0.0000
3.8 1.0542±0.0718 1.0488±0.0434 1.0615±0.0835
4.7 1.0738±0.0617 1.0640±0.0540 1.0847±0.0711
6.1 1.0984±0.0676 1.1184±0.0628 1.1068±0.0860
Table 1.6: Reaction time NORM average values with PROPGATED ERROR (s)
Effective Mass (kg) 2a 2b 2c
2.5 1.0000±0.0747 1.0000±0.0404 1.0000±0.0267
3.8 1.0542±0.1158 1.0488±0.0409 1.0615±0.0342
4.7 1.0738±0.0903 1.0640±0.0416 1.0847±0.0303
6.1 1.0984±0.0899 1.1184±0.0418 1.1068±0.0357

There is an overall effect of mass on reaction_time (slope = 2.607e-02, p = 0.000e+00).

Experiment 2b reaction_time is not different from 2a (p = 4.493e-01).

Experiment 2c reaction_time is not different from 2a (p = 9.755e-01).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_time did NOT change with mass more than 2a. (p = 1.892e-01).

Experiment 2c reaction_time did NOT change with mass more than 2a. (p = 5.748e-01).

Reaction Time by experiment.

Figure 1.5: Reaction Time by experiment.

1.4.2 Reaction Velocity

Table 1.7: Reaction Velocity linear models.
Reaction Velocity Linear Estimate P-Value Std Error
Circle 1.028e-04 1.329e-01 6.838e-05
Pilot 2.559e-04 8.326e-05 6.504e-05
Arc 3.021e-04 1.109e-04 7.816e-05
All 2.213e-04 5.632e-08 4.076e-05
Table 1.7: Reaction velocity average values, NO propgated error (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 -5.649e-04±2.801e-03 -2.308e-03±3.649e-03 -1.598e-03±2.942e-03
3.8 -6.079e-04±2.993e-03 -1.914e-03±3.095e-03 -1.265e-03±2.660e-03
4.7 -1.601e-04±2.137e-03 -1.422e-03±2.856e-03 -8.780e-04±2.124e-03
6.1 -2.491e-04±2.646e-03 -1.242e-03±2.679e-03 -6.478e-04±2.186e-03
Table 1.7: Reaction time velocity average values (m/s). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 -0.0006±0.0011 -0.0023±0.0022 -0.0016±0.0017
3.8 -0.0006±0.0016 -0.0019±0.0018 -0.0013±0.0012
4.7 -0.0002±0.0012 -0.0014±0.0014 -0.0009±0.0014
6.1 -0.0003±0.0020 -0.0012±0.0010 -0.0007±0.0014
Table 1.7: Reaction time velocity NORM average values with PROPGATED ERROR (s)
Effective Mass (kg) 2a 2b 2c
2.5 -0.0006±0.0028 -0.0023±0.0018 -0.0016±0.0013
3.8 -0.0006±0.0030 -0.0019±0.0015 -0.0013±0.0011
4.7 -0.0002±0.0021 -0.0014±0.0014 -0.0009±0.0009
6.1 -0.0003±0.0026 -0.0012±0.0013 -0.0007±0.0009

There is NOT an overall effect of mass on reaction_ (p = 2.407e-01).

Experiment 2b reaction_ is significantly lower than 2a (slope = -2.237e-03, p = 1.427e-03).

Experiment 2c reaction_ is significantly lower than 2a (slope = -1.437e-03, p = 2.498e-02).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_ increases with mass more than experiment 2a (slope = 2.144e-04, p = 4.583e-02).

Experiment 2c reaction_ did NOT change with mass more than 2a. (p = 8.859e-02).

Reaction by experiment.

Figure 1.6: Reaction by experiment.

1.4.3 Reaction Time Algorithm

These next plots are made to try and show the effect of reaction time algorithms on reaction. Figure 1.7 shows the reaction time by experiment and algorithm. Figure @ref(fig:reactiontanvelalgoplot1} shows the velocity at reaction time by the experiments and algorithms. This plot shows that my algorithm is detecting movement onset at very very low movement speeds, whereas other methods detect it at MUCH higher movement speeds.

Reaction Time Algorithm method.

Figure 1.7: Reaction Time Algorithm method.

Reaction Velocity Algorithm method.

Figure 1.8: Reaction Velocity Algorithm method.

1.5 Reaction Time Percent

Table 1.8: Reaction Time % linear models.
Reaction Time % Linear Estimate P-Value Std Error
Circle -3.695e-03 7.220e-11 5.670e-04
Pilot -8.975e-03 0.000e+00 6.127e-04
Arc -2.735e-03 1.738e-07 5.234e-04
All -5.642e-03 0.000e+00 3.427e-04
Table 1.8: Reaction % time average values, NO propogated error ALL AVG (s)
Effective Mass (kg) 2a 2b 2c
2.5 0.243±0.022 0.254±0.024 0.322±0.028
3.8 0.236±0.026 0.248±0.022 0.302±0.027
4.7 0.233±0.023 0.245±0.021 0.296±0.026
6.1 0.228±0.02 0.244±0.02 0.286±0.024
Table 1.8: Reaction Time percent average values (s). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 0.2425±0.0228 0.2539±0.0322 0.3210±0.0600
3.8 0.2355±0.0253 0.2480±0.0299 0.3018±0.0473
4.7 0.2334±0.0254 0.2449±0.0269 0.2957±0.0550
6.1 0.2279±0.0195 0.2440±0.0238 0.2854±0.0488
Table 1.8: Reaction time percent NORM average values with PROPGATED ERROR (s)
Effective Mass (kg) 2a 2b 2c
2.5 0.2425±0.0207 0.2539±0.0111 0.3210±0.0105
3.8 0.2355±0.0249 0.2480±0.0102 0.3018±0.0106
4.7 0.2334±0.0218 0.2449±0.0100 0.2957±0.0098
6.1 0.2279±0.0194 0.2440±0.0096 0.2854±0.0090

There is an overall effect of mass on reaction_time (slope = -3.637e-03, p = 1.106e-08).

Experiment 2b reaction_time is not different from 2a (p = 5.625e-01).

Experiment 2c reaction_time is significantly greater than 2a (slope = 9.070e-02, p = 6.258e-10).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_time increases with mass more than experiment 2a (slope = 8.950e-04, p = 3.211e-01).

Experiment 2c reaction_time decreases with mass more than experiment 2a (slope = -5.340e-03, p = 1.000e-10).

Reaction Time by experiment.

Figure 1.9: Reaction Time by experiment.

1.6 Endpoint Error

Table 1.9: Miss Distance linear models.
Miss Distance Linear Estimate P-Value Std Error
Circle -7.373e-05 4.278e-03 2.581e-05
Pilot 1.002e-03 0.000e+00 9.763e-05
Arc -1.478e-04 5.039e-06 3.240e-05
All 3.547e-04 1.998e-15 4.469e-05
Table 1.9: Miss Distance average values, NO propogated error ALL AVG (cm)
Effective Mass (kg) 2a 2b 2c
2.5 0.661±0.104 0.914±0.15 12.932±0.497
3.8 0.647±0.109 0.851±0.137 13.181±0.483
4.7 0.638±0.109 0.877±0.144 13.365±0.513
6.1 0.633±0.107 0.844±0.135 13.269±0.493
Table 1.9: Miss Distance average values (cm). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 0.0066±0.0014 0.0092±0.0023 0.1292±0.0142
3.8 0.0065±0.0014 0.0085±0.0018 0.1317±0.0133
4.7 0.0064±0.0016 0.0088±0.0020 0.1336±0.0143
6.1 0.0063±0.0014 0.0084±0.0018 0.1326±0.0137
Table 1.9: Miss Distance average values with PROPGATED ERROR (cm)
Effective Mass (kg) 2a 2b 2c
2.5 0.6605±0.0968 0.9153±0.0680 12.9228±0.1605
3.8 0.6466±0.1016 0.8513±0.0643 13.1727±0.1608
4.7 0.6369±0.1003 0.8777±0.0667 13.3561±0.1694
6.1 0.6335±0.1002 0.8441±0.0628 13.2610±0.1627

There is NOT an overall effect of mass on endpoint error (p = 2.960e-01).

Experiment 2b endpoint error is not different from 2a (p = 4.829e-01).

Experiment 2c endpoint error is significantly greater than 2a (slope = 1.206e-01, p = 0.000e+00).

The interesting thing with these are the interaction effects.

Experiment 2b endpoint error decreases with mass more than experiment 2a (slope = -6.361e-05, p = 5.881e-01).

Experiment 2c endpoint error increases with mass more than experiment 2a (slope = 1.085e-03, p = 0.000e+00).

Miss Distance (cm) by experiment.

Figure 1.10: Miss Distance (cm) by experiment.

Movement Duration by experiment.

(#fig:missdist_normbyexperiment)Movement Duration by experiment.

1.6.1 Endpoint Error Norm

Table 1.10: Miss Distance Norm linear models.
Miss Distance Norm Linear Estimate P-Value Std Error
Circle -1.154e-02 3.186e-03 3.913e-03
Pilot 8.268e-03 0.000e+00 7.304e-04
Arc -1.242e-02 5.118e-04 3.575e-03
All -3.381e-03 3.159e-02 1.573e-03
Table 1.10: Miss Distance Norm average values, NO propogated error ALL AVG (m)
Effective Mass (kg) 2a 2b 2c
2.5 100±14.64 100±14.613 100±2.748
3.8 98.249±15.688 94.892±14.548 102.194±3.143
4.7 96.158±15.267 96.785±14.624 103.581±3.337
6.1 95.886±15.303 94.044±14.374 102.817±3.158
Table 1.10: Miss Distance NORM average values (cm). Mean = mean of subject means. SE = SE of subject means.
Effective Mass (kg) 2a 2b 2c
2.5 1.0000±0.0000 1.0000±0.0000 1.0000±0.0000
3.8 0.9828±0.1035 0.9493±0.1307 1.0217±0.0599
4.7 0.9615±0.0816 0.9683±0.0963 1.0357±0.0671
6.1 0.9594±0.0875 0.9410±0.1344 1.0282±0.0586
Table 1.10: Miss Distance NORM average values with PROPGATED ERROR (cm)
Effective Mass (kg) 2a 2b 2c
2.5 100.0000±14.6784 100.0000±7.3208 100.0000±1.1792
3.8 98.2825±15.4628 94.9252±7.0642 102.1686±1.2122
4.7 96.1539±15.1376 96.8256±7.2042 103.5713±1.2697
6.1 95.9392±15.1536 94.0987±6.9610 102.8244±1.2254

There is an overall effect of mass on endpoint error (slope = -1.131e-02, p = 1.089e-04).

Experiment 2b endpoint error is not different from 2a (p = 7.209e-01).

Experiment 2c endpoint error is not different from 2a (p = 1.568e-01).

The interesting thing with these are the interaction effects.

Experiment 2b endpoint error did NOT change with mass more than 2a. (p = 7.684e-01).

Experiment 2c endpoint error increases with mass more than experiment 2a (slope = 1.954e-02, p = 2.545e-07).

Miss Distance Norm (cm) by experiment.

Figure 1.11: Miss Distance Norm (cm) by experiment.

1.7 Angular Variance

Table 1.11: Miss Distance linear models.
Miss Distance Linear Estimate P-Value Std Error
Circle 2.200e-01 6.441e-01 4.762e-01
Pilot 2.013e+00 4.722e-01 2.799e+00
Arc -2.758e-01 6.754e-01 6.588e-01
All 8.466e-01 4.873e-01 1.219e+00
Table 1.11: Miss Angle Variance average values (deg^2)
Effective Mass (kg) 2a 2b 2c
2.5 3.326±0.436 20.073±4.746 86.234±15.391
3.8 2.908±0.382 15.926±3.185 95.583±25.458
4.7 6.011±2.838 20.423±4.499 91.745±18.894
6.1 3.42±0.408 17.868±3.325 95.2±18.735

There is NOT an overall effect of mass on miss angle variance (p = 9.235e-01).

Experiment 2b miss angle variance is not different from 2a (p = 5.163e-01).

Experiment 2c miss angle variance is significantly greater than 2a (slope = 8.037e+01, p = 6.922e-04).

The interesting thing with these are the interaction effects.

Experiment 2b miss angle variance decreases with mass more than experiment 2a (slope = -4.958e-01, p = 8.784e-01).

Experiment 2c miss angle variance did NOT change with mass more than 2a. (p = 5.446e-01).

Miss Angle Variance (deg^2) by experiment.

Figure 1.12: Miss Angle Variance (deg^2) by experiment.

1.8 Radial Variance

Table 1.12: Miss Distance Radial Variance (cm^2) linear models.
Miss Distance Linear Estimate P-Value Std Error
Circle -4.352e-03 3.409e-01 4.570e-03
Pilot 3.246e-01 1.838e-03 1.042e-01
Arc -9.412e-03 2.239e-03 3.079e-03
All 1.352e-01 3.875e-03 4.680e-02
Table 1.12: Miss Radial Variance average values (cm^2)
Effective Mass (kg) 2a 2b 2c
2.5 0.2808±0.0167 0.2528±0.0173 1.518±0.5973
3.8 0.2602±0.0139 0.2314±0.0154 2.015±0.5981
4.7 0.267±0.0241 0.226±0.0202 2.4844±0.4862
6.1 0.2618±0.0223 0.2165±0.013 2.7002±0.4948

There is NOT an overall effect of mass on miss radial variance (p = 9.586e-01).

Experiment 2b miss radial variance is not different from 2a (p = 9.859e-01).

Experiment 2c miss radial variance is not different from 2a (p = 5.075e-01).

The interesting thing with these are the interaction effects.

Experiment 2b miss radial variance did NOT change with mass more than 2a. (p = 9.660e-01).

Experiment 2c miss radial variance increases with mass more than experiment 2a (slope = 3.289e-01, p = 2.367e-03).

Miss Radial Variance by experiment.

Figure 1.13: Miss Radial Variance by experiment.

Miss Rad Variance (cm^2) broken by experiment.

Figure 1.14: Miss Rad Variance (cm^2) broken by experiment.

1.9 Resample Plots

## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
Velocity trajectories by experiment.

Figure 1.15: Velocity trajectories by experiment.

Velocity trajectories by experiment.

Figure 1.16: Velocity trajectories by experiment.

1.9.1 One Subject

1.9.1.1 2a

1.9.1.2 2b

1.9.1.3 2c

1.10 Resample Plots TANV

## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
Velocity trajectories by experiment.

Figure 1.17: Velocity trajectories by experiment.

Velocity trajectories by experiment.

Figure 1.18: Velocity trajectories by experiment.

1.10.1 One Subject

1.10.1.1 2a

1.10.1.2 2b

1.10.1.3 2c

1.11 Resamp Compared

Even though the preferred looks the same, just turns out the two velocity profiles are REALLY REALLY similar, but slightly different. This is shown in the following plot, that is zoomed into the peak velocities.

1.12 Preferred Experiment Grouped Plots

1.12.1 Grouped

2 Metabolics Experiment

We filtered the metabolic data and removed any trial where the miss distance at endpoint was greater than 10 cm, the movement duration was less than 0.2 seconds, or the reaction time was greater than 0.50 s.This removed 13 out of 15975 original data points.

2.0.1 Speed on speed

## Analysis of Variance Table
## 
## Response: movedur
##              Df  Sum Sq Mean Sq    F value Pr(>F)    
## speed         1 1099.40 1099.40 1.0453e+05 <2e-16 ***
## eff_mass2     1    0.01    0.01 6.3430e-01 0.4258    
## Residuals 15959  167.85    0.01                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = movedur ~ speed + eff_mass2 + (1 | subj), data = metdata_factor)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 2.498e-01  8.172e-03  30.571   <2e-16 ***
## speed == 0       1.544e-01  4.760e-04 324.257   <2e-16 ***
## eff_mass2 == 0   5.641e-06  2.371e-04   0.024    0.981    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

2.1 MP Gross

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(metpowergross) ~ log(movedur) + effmass2 + 
##     (1 | subject), data = mpdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   4.561517   0.066021  69.092  < 2e-16 ***
## log(movedur) == 0 -0.766794   0.037690 -20.345  < 2e-16 ***
## effmass2 == 0      0.017373   0.003369   5.156 2.52e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
## NULL
Table 2.1: Gross Metabolic power plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 171.9775 ± 18.515 131.625 ± 14.3282 110.1838 ± 5.8343 98.8513 ± 7.9976 105.3988 ± 8.8935 99.835 ± 7.0959 NaN ± NA
4.83 kg 187.4712 ± 17.3187 153.6538 ± 13.0638 126.0213 ± 8.2191 104.4825 ± 6.9769 97.5825 ± 7.3818 97.2367 ± 5.4622 NaN ± NA
7.13 kg NaN ± NA 185.5288 ± 19.5249 140.2988 ± 11.6277 112.705 ± 6.8381 109.9457 ± 8.6896 98.7512 ± 7.5674 93.9238 ± 7.265
11.69 kg NaN ± NA 222.0612 ± 24.3934 155.0838 ± 13.5348 117.4025 ± 10.6555 110.285 ± 10.4558 96.8338 ± 5.2816 92.7812 ± 6.6335
Gross metabolic power.

Figure 2.1: Gross metabolic power.

Parameter estimates are showing as mean +- standard error. The columns are for without the subject mass coefficient, and with a mass coefficient on the effort model. Subj Mass Coef is the subject mass exponent.

The no_mass_coef model is as follows: \[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

The Subject mass model times a1 is as follows: \[ \dot{e} = a*Body Mass^{f}+\frac{bm^c}{T_m^d} \]

The effective mass model times a1 is as follows: \[ \dot{e} = a*Effective\, Mass^{f}+\frac{bm^c}{T_m^d} \]

Table 2.2: Gross metabolic power coefficients.
a only a*subject mass a*effective mass
a 98.2501±3.0512 22.0844±13.6907 101.4027±7.5926
b 0.864±0.4319 0.8593±0.4234 0.8375±0.4215
c 0.8308±0.0998 0.8247±0.0981 0.8548±0.1107
d 5.8254±0.603 5.8562±0.5956 5.8035±0.6061
f null 0.2983±0.1232 -0.0187±0.0411
SSE 120872.749595644 116826.723834405 120743.074844557
AIC 1750.832 1746.4653 1752.6313
BIC 1766.9875 1765.852 1772.0179

2.2 MP net

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(metpowernet) ~ log(movedur) + effmass2 + (1 | 
##     subject), data = mpdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   2.85218    0.23454  12.161  < 2e-16 ***
## log(movedur) == 0 -2.37941    0.16610 -14.326  < 2e-16 ***
## effmass2 == 0      0.04912    0.01485   3.308  0.00094 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.3: Net Metabolic power plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 99.075 ± 17.3755 57.7875 ± 15.0154 36.3125 ± 5.9248 24.9875 ± 6.1351 31.5325 ± 8.1858 27.9333 ± 5.6508 NaN ± NA
4.83 kg 113.7375 ± 18.2929 79.9875 ± 13.8077 52.3875 ± 8.9795 30.8212 ± 5.8168 23.9213 ± 7.2462 24.4667 ± 4.0208 NaN ± NA
7.13 kg NaN ± NA 111.7875 ± 19.9953 65.4 ± 11.9993 37.8638 ± 7.2397 37.7043 ± 7.8668 23.8963 ± 6.5959 19.0538 ± 6.8651
11.69 kg NaN ± NA 150.475 ± 22.0585 83.35 ± 13.048 45.6812 ± 10.4043 38.5625 ± 9.4318 25.0825 ± 5.0728 21.0525 ± 5.3099
Net metabolic power.

Figure 2.2: Net metabolic power.

Parameter estimates are showing as mean +- standard error. The columns are for without the subject mass coefficient, and with a mass coefficient on the effort model. Subj Mass Coef is the subject mass exponent.

The no_mass_coef model is as follows: \[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

The Subject mass model times a1 is as follows: \[ \dot{e} = a*Body Mass^{f}+\frac{bm^c}{T_m^d} \]

The effective mass model times a1 is as follows: \[ \dot{e} = a*Effective\, Mass^{f}+\frac{bm^c}{T_m^d} \]

Table 2.4: Net metabolic power coefficients.
a only a*subject mass a*effective mass
a 24.7227±2.9124 0.1006±0.2368 24.0136±7.0227
b 1.0308±0.467 1.0007±0.4474 1.031±0.4707
c 0.7964±0.0904 0.7942±0.089 0.7962±0.1007
d 5.6574±0.5473 5.7151±0.5413 5.6575±0.5519
f null 1.0939±0.4615 5e-04±0.1585
SSE 105365.400000357 101455.132835216 105365.395173997
AIC 1725.1562 1720.0843 1727.1561
BIC 1741.3117 1739.4709 1746.5428

2.3 MCost Gross

Table 2.5: Gross Metabolic Cost plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 93.3222 ± 8.9748 80.1472 ± 7.2013 82.5764 ± 3.4054 94.0607 ± 9.0851 117.4043 ± 9.7673 125.4443 ± 10.8215 NaN ± NA
4.83 kg 104.3653 ± 7.7764 95.0103 ± 5.6431 96.0467 ± 6.7137 97.5592 ± 7.0411 109.7052 ± 8.5622 123.3466 ± 10.6279 NaN ± NA
7.13 kg NaN ± NA 108.7596 ± 10.3474 95.2653 ± 7.1374 96.7068 ± 6.2899 113.0375 ± 8.3502 120.2383 ± 9.9578 130.8822 ± 10.7193
11.69 kg NaN ± NA 134.6313 ± 12.7635 106.7865 ± 8.1232 101.0186 ± 8.5022 112.9603 ± 9.2217 118.1752 ± 7.0501 128.0428 ± 9.1786
Gross metabolic cost.

Figure 2.3: Gross metabolic cost.

The linear slope of the metabolic minimum is 0.0170765.

The optimal movement durations using the preferred masses are shown below along with the average movement durations.

Table 2.6: Optimal durations for gross metabolic cost from metabolics exp.
Effective Mass (kg) Minimum Cost Duration (s) Minimum Cost (J)
a1 2.44 0.6627202 78.60625
a1 4.83 0.7277517 86.31782
a1 7.13 0.7693100 91.24823
a1 11.69 0.8254945 97.91511
Table 2.6: Optimal durations for gross metabolic cost from pref. exp. 2a
Effective Mass (kg) Minimum Cost (J) Minimum Cost Duration (s) Preferred Duraiton (s)
a1 2.506 78.60625 0.6627202 0.7806626
a1 3.959 83.90409 0.7073980 0.8441430
a1 4.894 86.48003 0.7291192 0.8676516
a1 5.282 89.61512 0.7555548 0.9044893

2.4 MCost Net

Table 2.7: Net Metabolic Cost plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 53.1932 ± 8.5657 34.0816 ± 8.4267 26.267 ± 3.4663 23.2311 ± 5.6268 33.9323 ± 8.6921 35.0672 ± 7.0593 NaN ± NA
4.83 kg 62.5789 ± 9.018 48.3557 ± 6.9453 39.0854 ± 6.5272 27.9088 ± 5.0761 25.9021 ± 7.7596 31.196 ± 5.3426 NaN ± NA
7.13 kg NaN ± NA 65.0537 ± 11.2371 44.2351 ± 7.8498 32.5745 ± 6.4326 38.6832 ± 7.8991 29.137 ± 8.1055 26.4202 ± 9.651
11.69 kg NaN ± NA 90.9807 ± 11.7824 57.1 ± 8.418 39.0674 ± 8.6669 38.9813 ± 8.9591 30.4859 ± 6.2224 28.82 ± 7.2275
Net metabolic cost.

Figure 2.4: Net metabolic cost.

The optimal movement durations using the preferred masses are shown below along with the average movement durations.

Table 2.8: Minimum Cost durations for net metabolic cost.
Effective Mass (kg) Minimum Cost (J) Minimum Cost Duration (s) Preferred Duraiton (s)
a1 2.506 25.58113 0.8518398 0.7806626
a1 3.959 27.28208 0.9084598 0.8441430
a1 4.894 28.10861 0.9359942 0.8676516
a1 6.282 29.11412 0.9694671 0.9044893

2.5 Table of Movement Durations

Table 2.9: Movement Duration plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 0.5486 ± 0.014 0.6202 ± 0.0211 0.7576 ± 0.0325 0.951 ± 0.0419 1.1227 ± 0.0476 1.2528 ± 0.04 NaN ± NA
4.83 kg 0.5644 ± 0.0145 0.6295 ± 0.0219 0.7677 ± 0.0355 0.9386 ± 0.0381 1.1305 ± 0.0416 1.2593 ± 0.0459 NaN ± NA
7.13 kg NaN ± NA 0.5921 ± 0.011 0.6819 ± 0.007 0.8569 ± 0.0082 1.0306 ± 0.0152 1.2143 ± 0.0205 1.3931 ± 0.0269
11.69 kg NaN ± NA 0.6114 ± 0.0113 0.6931 ± 0.0115 0.8638 ± 0.0102 1.0304 ± 0.0163 1.2184 ± 0.0144 1.38 ± 0.013

2.6 Endpoint Error

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(miss_dist) ~ log(movedur) + eff_mass2 + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  -5.529646   0.058862  -93.94   <2e-16 ***
## log(movedur) == 0 -0.937237   0.017751  -52.80   <2e-16 ***
## eff_mass2 == 0     0.021596   0.001683   12.83   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.10: Endpoitn Error plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
4.83 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
7.13 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
11.69 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA 
## `geom_smooth()` using formula = 'y ~ x'
Endpoint Error.

Figure 2.5: Endpoint Error.

2.7 Angle Variance

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(missangle) ~ log(movedur) + eff_mass + (1 | 
##     subj), data = c)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   0.725112   0.110989   6.533 6.44e-11 ***
## log(movedur) == 0 -1.140494   0.074464 -15.316  < 2e-16 ***
## eff_mass == 0      0.017010   0.006734   2.526   0.0115 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.11: Miss Angle Variance plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 1.1816±,0.3227 0.8386±,0.3227 0.7531±,0.3227 0.5641±,0.3227 0.4743±,0.3227 0.4589±,0.3227 0.5233±,0.3227
4.83 kg 1.2879±,0.3506 0.9431±,0.3506 0.7494±,0.3506 0.6479±,0.3506 0.5246±,0.3506 0.5009±,0.3506 0.547±,0.3506
7.13 kg ±, 1.0496±,0.3291 0.8785±,0.3291 0.652±,0.3291 0.511±,0.3291 0.4353±,0.3291 0.4983±,0.3291
11.69 kg ±, 1.2156±,0.3427 0.9214±,0.3427 0.6676±,0.3427 0.53±,0.3427 0.452±,0.3427 0.493±,0.3427 
## `geom_smooth()` using formula = 'y ~ x'
Angular miss variance.

Figure 2.6: Angular miss variance.

2.8 Radial Endpoint Variance

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(miss_rad) ~ log(movedur) + eff_mass + (1 | 
##     subj), data = c)
## 
## Linear Hypotheses:
##                     Estimate Std. Error  z value Pr(>|z|)    
## (Intercept) == 0  -10.560240   0.086391 -122.237   <2e-16 ***
## log(movedur) == 0  -1.000088   0.070361  -14.214   <2e-16 ***
## eff_mass == 0      -0.006766   0.006364   -1.063    0.288    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.12: Radial Endpoint Variance plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 0.3286±,0.0772 0.2452±,0.0943 0.212±,0.056 0.1659±,0.0119 0.1802±,0.0322 0.1666±,0.0096 0.1983±,0.0012
4.83 kg 0.3244±,0.0778 0.2426±,0.0473 0.1943±,0.0302 0.1928±,0.0334 0.1793±,0.023 0.1752±,0.012 0.183±,0.0184
7.13 kg ±, 0.2456±,0.0572 0.2012±,0.0684 0.1834±,0.0723 0.1603±,0.0278 0.1578±,0.014 0.1647±,0.0191
11.69 kg ±, 0.2745±,0.0397 0.1985±,0.013 0.1776±,0.0235 0.1613±,0.0264 0.1564±,0.0164 0.1619±,0.0177 
## `geom_smooth()` using formula = 'y ~ x'
Radial miss variance.

Figure 2.7: Radial miss variance.

2.9 Reaction Time

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv ~ log(movedur) + eff_mass2 + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  0.1585730  0.0071557   22.16   <2e-16 ***
## log(movedur) == 0 0.0530319  0.0012279   43.19   <2e-16 ***
## eff_mass2 == 0    0.0023967  0.0001164   20.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv ~ movedur + eff_mass2 + (1 | subj), 
##     data = metdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 0.0924072  0.0072719   12.71   <2e-16 ***
## movedur == 0     0.0643985  0.0014023   45.92   <2e-16 ***
## eff_mass2 == 0   0.0023962  0.0001155   20.75   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.13: Reaction time plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
4.83 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
7.13 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
11.69 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA 
## `geom_smooth()` using formula = 'y ~ x'
Reaction time in metabolic experiment.

Figure 2.8: Reaction time in metabolic experiment.

2.9.1 Reaction Time %

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv_perc ~ log(movedur) + eff_mass2 + 
##     (1 | subj), data = metdata)
## 
## Linear Hypotheses:
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   0.1563571  0.0092862   16.84   <2e-16 ***
## log(movedur) == 0 -0.1432859  0.0016273  -88.05   <2e-16 ***
## eff_mass2 == 0     0.0028230  0.0001543   18.30   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv_perc ~ movedur + eff_mass2 + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  0.3192568  0.0093404   34.18   <2e-16 ***
## movedur == 0     -0.1536866  0.0019291  -79.67   <2e-16 ***
## eff_mass2 == 0    0.0025781  0.0001589   16.23   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.14: Reaction time plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
4.83 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
7.13 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA
11.69 kg NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA NaN ± NA 
## `geom_smooth()` using formula = 'y ~ x'
Reaction time in metabolic experiment.

Figure 2.9: Reaction time in metabolic experiment.

2.10 Metabolic results plot

Metabolic experiment results.

Figure 2.10: Metabolic experiment results.

3 Effort models

We compute 4 effort models here. Gross metabolics, net metabolics, and sum of torque squared (experimentally calculated and calcualted from minimum jerk). Net and gross metabolics have been addressed before, here we add sum of torque squared.

Sum of torque squared is calcualted from the data and simulated minimum jerk profiles and then fit to an effort model like net metabolic and gross metabolic power but without the a parameter.

\[ \dot{e} = \frac{bm^c}{T_m^d} \]

The parameters fit for the effort models are shown in table @ref(tab:effort_prarms).

3.1 Torque Squared

Sum of torque squared fits from the data

Figure 3.1: Sum of torque squared fits from the data

3.2 Effort model parameters

This table shows a summary of all the parameters that were fitted in the effort models. SSE, AIC, and BIC can be found in their respective sections.

Table 3.1: Parameters fit in the effort models.
Net Metabolics Gross Metabolics Torque\(^2\) Torque\(^2\) minjerk
a0 73.3259±3.6041 73.3259±3.6041 0 0
a 24.0346 ± 2.9124 98.2501 ± 3.0512 0 0
b 1.0308 ± 0.467 0.864 ± 0.4319 0.0136 ± 0.0028 0.0554 ± 0.0259
c 0.7964 ± 0.0904 0.8308 ± 0.0998 2.3415 ± 0.0706 2.2988 ± 0.1687
d 5.6574 ± 0.5473 5.8254 ± 0.603 5.0157 ± 0.1792 1.2333 ± 0.0614
SSE 105365.400000357 120872.749595644 1509.56505066476 118250.243680345
AIC 1725.15615301424 1750.8320060654 853.626308139953 1917.62664958662
BIC 1741.31169609851 1766.98754914967 866.122164057567 1930.97680190542

3.2.1 Torque squared models with offset not forced to 0

Sum of torque squared is calculated from the data and simulated minimum jerk profiles and then fit to an effort model like net metabolic and gross metabolic power. In these we allowed \(a\) to be fit to see if it would predict a 0 offset.

\[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

This table shows the confident intervals on the torque with \(a\) model. The probability of \(a\) (\(a_1\)) being greater than 0 is 0.0015173.

Table 3.2: Confidence intervals for torque squared model.
2.5% 97.5%
a1 -1.2296995 0.2214529
a2 0.0100917 0.0294421
a3 2.1176112 2.4417127
a4 4.4647333 5.2767459

4 Probablity Modeling

The probability function for the 2a is: \[ ln\left(\frac{P_i}{1-P_i}\right) = \beta_0 + \beta_1 x_1 \] Which leads to \[ P(Success|T) = \frac{1}{1+e^{-(\beta_0) - (\beta_1)T}} \] Mass is removed from this probability as according to the model it is insignificant. Duration and mass also conditions here, so we only use duration. I leave it \(\beta_1\) because that is more similar to the glm with mass from experiment 1.

We then use this function to first fit an inverse logit to experiment 2a and 2b. We then use the criteria for success and fit the same inverse logit function but using the data from experiment 1.

4.1 Probability of sucess in just 2a and 2b without 1

The following table shows the beta coefficients for the inverse logit function only predicting from experiment 2a and 2b.

Table 4.1: Beta coefficient for the inverse logit function to predict probability of success.
2a 2b
\(\beta_0\) 3.3276 ± 0.264 1.8785 ± 0.125
\(\beta_1\) -0.1023 ± 0.303 -0.4024 ± 0.133

Using these functions we can then predict the probability of success as a fraction of success given the data and using the logit model. The following table shows this for experiment 2a and 2b.

Table 4.2: Success probabilities for experiment 2a and 2b. Also predicted from glm fitted using data from 2a and 2b
2a Predicted 2a 2b Predicted 2b
2.506 0.9606 0.9626 0.7928 0.8232
3.959 0.9623 0.9624 0.8487 0.8199
4.894 0.9612 0.9623 0.8083 0.8184
6.282 0.9651 0.9621 0.8260 0.8156

We can also estimate the probability on the standard deviation of the miss distance.

Table 4.3: Success probabilities for experiment 2a and 2b. Also predicted from glm fitted using data from 2a and 2b. 2b Is off cause i havn’t done the joint probability yet.
2a Predicted 2a 2b Predicted 2b
2.506 0.9606 0.9797 0.7928 0.9797
3.959 0.9623 0.9772 0.8487 0.9772
4.894 0.9612 0.9780 0.8083 0.9780
6.282 0.9651 0.9805 0.8260 0.9805

4.1.1 2a and 2b GLM probability plots

The plot below shows the fits of the glm’s fitted to only data from experiment 2a and 2b. Unfortunately, these glm’s don’t seem to have the same behavior as data fitted to experiment 1 of dropping off to 0 at faster speeds. This is probably due to the lack of really fast or really slow trials so it just predicts a flat line essentially.

Probability of success with glm fitted to experiment 2a and 2b data.

Figure 4.1: Probability of success with glm fitted to experiment 2a and 2b data.

4.2 Probability of success using experiment 1

\[ P(Success|T) = \frac{1}{1+e^{-(\beta_0) - (\beta_1)T - (\beta_2)m}} \]

This table shows the beta coefficients when using an inverse logit on experiment 1 trying to predict 2a and 2b.

Table 4.4: Beta coefficient for the inverse logit function to predict probability of success.
2a 2b
\(\beta_0\) -1.4496 ± 0.125 -2.9312 ± 0.091
\(\beta_1\) 5.8768 ± 0.188 6.0912 ± 0.129
\(\beta_2\) -0.0946 ± 0.008 -0.0828 ± 0.006

This plot only includes movement durations that are seen in the metabolic experiment. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

Figure 4.2: Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

This plot includes low and high movement durations to show that the functions converge to 0 and 1 probability respectively.

Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

Figure 4.3: Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

This next table shows the movement durations for experiment 2a and 2b, the probability of success from the experiment, along with the probability of success from the logistic regression. The last row is the mean probability.

2a Movedur 2a Exp Prob 2a Pred Prob 2b Movedur 2b Exp Prob 2b Pred Prob
2.506 0.7807 0.9606 0.9479 0.8457 0.7928 0.8821
3.959 0.8441 0.9623 0.9584 0.9018 0.8487 0.9033
4.894 0.8677 0.9612 0.9603 0.9262 0.8083 0.9093
6.282 0.9045 0.9651 0.9634 0.9733 0.8260 0.9225
Mean NaN 0.9623 0.9575 NaN 0.8189 0.9043

4.2.1 Success at metabolically optimal

The table (@ref{tab:optdurprob}) shows the metabolically optimal (gross) durations with the predicted probabilities from the glm using experiment 1 and 2a.

Table 4.5: Success probabilites from experiment 2a/1 at the metabolically optimal duraitons.
Effective.Mass Duration Success.Prob
2.44 0.6627202 0.9015146
4.83 0.7073980 0.9046978
7.13 0.7291192 0.8966490
11.69 0.7555548 0.8681094

4.3 Predicting movedur off of probability

The probability of reward that minimizes the error of predicted movement durations for the 2a experiment is 0.958. The table below shows the predicted movement durations and the expected movement durations. The SSE of this prediction is 0.0021639.

Table 4.6: Predicted movement durations for the 2a given probability of: 0.958
Effective Mass (kg) Predicted Duration Preferred Duration
2.506 0.819 0.78
3.959 0.843 0.843
4.894 0.858 0.867
6.282 0.88 0.904

The probability of reward that minimizes the error of predicted movement durations for the 2a experiment is 0.9053. The table below shows hte predicted movement durations and the expected movement durations. The SSE of this prediction is 0.017531.

Table 4.7: Predicted movement durations for the 2b given probability of: 0.9053
Effective Mass (kg) Predicted Duration Preferred Duration
2.506 0.886 0.846
3.959 0.906 0.902
4.894 0.919 0.927
6.282 0.938 0.973

5 Utility Modeling

5.1 Individual Utility

This plot below shows individual subjects and their utility fits. This uses gross metabolics as the effort term.

The average fitted \(\alpha\) value was 48.1075.

Utility fits by subject.

Figure 5.1: Utility fits by subject.

5.2 Utility Code

5.2.1 Combined utility code

5.3 Table for the coefficients in Utility Modeling

We next fitted a utility model by altering \(\alpha\) to try and predict the movement durations seen in 2a,b,c.

The utility function that is fit for these next plots is below. \(T_r\) and \(T_m\) are the reaction time and movement duration. \(P(R|m,t)\) is determined from the section above, probability alpha modeling. \(a\), \(b\), \(c\), \(d\) are determined from the metabolic data. Resting rate is shown by \(a_0\), and \(a_0\) = 73.527. The parameters a, b, c, and d are shown in 3.1.

\[J = \frac{\alpha P(R|m,T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\] Ideally the probability function has an effect of mass in it, but for the following results we use the glm from experiment 2a/2b to fit \(\alpha\), which leads to the probability function only including a term of time.

\[J = \frac{\alpha P(R|T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\]

\(T_r\) and \(T_m\) are the reaction time and movement duration. Using the values from experiment 2a,b,c, we can optimize the error of the prediction by altering \(\alpha\).

The tables below show the movement durations (@ref{tab:utilmovedurstab}), reaction time (@ref{rab:utilreacttimestab}).

Table 5.1: Movement durations by experiement and effective mass used in the Utility model
2a 2b 2c
2.506 kg 0.781 0.846 0.667
3.959 kg 0.844 0.902 0.743
4.894 kg 0.868 0.926 0.782
6.282 kg 0.904 0.973 0.823
Table 5.2: Reaction times by experiement and effective mass used in the Utility model
2a 2b 2c
2.506 kg 0.184 0.208 0.201
3.959 kg 0.194 0.217 0.214
4.894 kg 0.198 0.220 0.219
6.282 kg 0.203 0.232 0.223

5.4 Experimental Utility Fits

FITTING Three ALPHA VALUEs, one to each experiment. ### 2a Alpha This table (??) shows the \(\alpha\) value, predicted duration for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later.

Table 5.3: Preferred duration and predicted durations for each model.
2a Experiment Net Metabolic Power Gross Metabolic power Utility (Net Power) Utility (Gross Power Torque\(^2\) Torque\(^2\) minjerk
Alpha 0 0 0 79.4094 54.4634 1.3106 31.1648
2.44 0.7807 0.8561 0.6627 0.785 0.785 0.617 0.74
4.83 0.8441 0.913 0.7074 0.84 0.84 0.777 0.81
7.13 0.8677 0.9407 0.7291 0.868 0.868 0.867 0.86
11.69 0.9045 0.9743 0.7556 0.903 0.903 0.989 0.96
SSE 0 2.064e-02 7.398e-02 3.832e-05 3.832e-05 3.844e-02 5.959e-03

The probability of success for utility in experiement 2a using the optimized alpha value are shown below.

Table 5.4: Probability of success used in utility modeling when fitting alpha, Expirement 2a.
Utility Net Utility Gross Utility Torque Utility Torque Mj
2.506 0.9491427 0.9491427 0.8742680 0.9347516
3.959 0.9573953 0.9573953 0.9394607 0.9495951
4.894 0.9603922 0.9603922 0.9601680 0.9585646
6.282 0.9631249 0.9631249 0.9774244 0.9733414

5.4.1 2b Alpha

This table (5.5) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2b}).

Table 5.5: Preferred duration and predicted durations for each model.
2b Experiment Net Metabolic Power Gross Metabolic power Utility (Net Power) Utility (Gross Power Torque\(^2\) Torque\(^2\) minjerk
Alpha 0 0 0 141.2476 80.2642 28.0457 98.0839
2.44 0.8457 0.8561 0.6627 0.865 0.862 0.75 0.85
4.83 0.9018 0.913 0.7074 0.904 0.904 0.803 0.88
7.13 0.9262 0.9407 0.7291 0.925 0.927 0.838 0.9
11.69 0.9733 0.9743 0.7556 0.955 0.958 0.889 0.93
SSE 0 4.426e-04 1.575e-01 7.144e-04 5.057e-04 3.381e-02 3.058e-03

The probability of success for utility in experiement 2b using the optimized alpha value are shown below.

Table 5.6: Probability of success used in utility modeling when fitting alpha, Expirement 2b.
Utility Net Utility Gross Utility Torque Utility Torque Mj
2.506 0.8938010 0.8920540 0.8068510 0.8848110
3.959 0.9044274 0.9044274 0.8364710 0.8910223
4.894 0.9087040 0.9097096 0.8542056 0.8952598
6.282 0.9141757 0.9155986 0.8769327 0.9014499

5.4.2 2c Alpha

This table (5.7) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2b}).

Table 5.7: Preferred duration and predicted durations for each model.
2c Experiment Net Metabolic Power Gross Metabolic power Utility (Net Power) Utility (Gross Power Torque\(^2\) Torque\(^2\) minjerk
Alpha 0 0 0 94.0121 75.1132 25.1875 22.0569
2.44 0.6673 0.8561 0.6627 0.692 0.691 0.529 0.01
4.83 0.7429 0.913 0.7074 0.748 0.746 0.694 0.05
7.13 0.7816 0.9407 0.7291 0.776 0.773 0.785 0.12
11.69 0.8234 0.9743 0.7556 0.811 0.807 0.927 0.88
SSE 0 1.127e-01 8.635e-03 8.203e-04 9.131e-04 3.227e-02 1.353e+00

The probability of success for utility in experiement 2b using the optimized alpha value are shown below.

Table 5.8: Probability of success used in utility modeling when fitting alpha, Expirement 2c.
Utility Net Utility Gross Utility Torque Utility Torque Mj
2.506 1 1 1 1
3.959 1 1 1 1
4.894 1 1 1 1
6.282 1 1 1 1
Utility fits across experiments.

Figure 5.2: Utility fits across experiments.

5.5 2a and 2b Combined Utility fits

This section analysis fits one \(\alpha\) value to experiment 2a and 2b at the same time. These next tables show the movement durations, predicted movement durations, the fitted alpha values, and the probabilities of success. The \(\alpha\) value for 2a and 2b are fit at once, so it is the same. 2c has its own \(\alpha\) value.

The \(\alpha\) value fitted here is 60.6779456. The SSE for experiment 2a/2b when using one alpha is 2.632e-03. The SSE for experiment 2c is 9.131e-04. The total SSE for all 3 is 3.545e-03.

Table 5.9: Experimental and predicted movement durations for the experiments.
2a Exp 2a pred 2b Exp 2b pred 2c Exp 2c pred
2.506 0.7806626 0.774 0.8456631 0.878 0.6673158 0.691
3.959 0.8441430 0.828 0.9018428 0.923 0.7428759 0.746
4.894 0.8676516 0.855 0.9262331 0.947 0.7815969 0.773
6.282 0.9044893 0.890 0.9732835 0.979 0.8233858 0.807
Table 5.10: Probabilites of success for the experiments.
2a 2b 2c
2.506 0.9459 0.9011 1
3.959 0.9544 0.9140 1
4.894 0.9574 0.9192 1
6.282 0.9603 0.9250 1
Table 5.11: Alpha values fitted to experiment 2a/2b, and a seperate alpha for 2c.
2a 2b 2c
lpha 60.678 60.678 75.113

5.5.1 Grouped plot

Utility fits across experiments.

Figure 5.3: Utility fits across experiments.

6 Different utility models

Utility 1: \[J = \frac{\alpha P(R|m,T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\]

Utility 2: \[J = \alpha P(R|m,T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)\]

Utility 3: \[J = \frac{\alpha P(R|m,T_m)}{T_r+T_m} -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)\]

Utility 4: \[J = \frac{P(R|m,T_m)}{a_0 T_r + a T_m + \frac{bm^c}{T_m^d}}\]

6.1 All random utility models

6.1.1 One Alpha value

Table 6.1: 2a - Movement duration by utility model for experiment 2a.
eff_mass Movement Duration (s) Utility 1 Gross Duration Utility 2 Gross Duration Utility 3 Gross Duration Utility 1 Net Duration Utility 2 Net Duration Utility 3 Net Duration Utility Comb 1 Gross Duration Utility Comb 2 Gross Duration Utility Comb 3 Gross Duration Utility Comb 1 Net Duration Utility Comb 2 Net Duration Utility Comb 3 Net Duration
alpha alpha 54.463 259.211 -94.223 79.409 -59.453 21.098 60.678 166.74 3.149 93.503 -7.803 20.122
2.506 0.7807 0.785 0.804 0.809 0.785 0.777 0.785 0.774 0.76 0.66 0.764 0.846 0.788
3.959 0.8441 0.84 0.84 0.841 0.84 0.841 0.842 0.828 0.799 0.705 0.816 0.904 0.844
4.894 0.8677 0.868 0.86 0.857 0.868 0.871 0.87 0.855 0.819 0.727 0.843 0.932 0.872
6.282 0.9045 0.903 0.886 0.875 0.903 0.906 0.904 0.89 0.846 0.753 0.877 0.966 0.907
SSE SSE 3.832e-05 9.622e-04 1.796e-03 3.832e-05 3.679e-05 2.916e-05 6.750e-04 8.253e-03 7.665e-02 2.433e-03 1.578e-02 7.907e-05
Table 6.1: 2b - Movement duration by utility model for experiment 2b.
eff_mass Movement Duration (s) Utility 1 Gross Duration Utility 2 Gross Duration Utility 3 Gross Duration Utility 1 Net Duration Utility 2 Net Duration Utility 3 Net Duration Utility Comb 1 Gross Duration Utility Comb 2 Gross Duration Utility Comb 3 Gross Duration Utility Comb 1 Net Duration Utility Comb 2 Net Duration Utility Comb 3 Net Duration
alpha alpha 80.264 142.685 982.678 141.248 -2.762 5.921 60.678 166.74 3.149 93.503 -7.803 20.122
2.506 0.8457 0.862 0.875 0.764 0.865 0.846 0.849 0.878 0.899 0.665 0.897 0.826 0.836
3.959 0.9018 0.904 0.905 0.793 0.904 0.904 0.903 0.923 0.928 0.709 0.939 0.886 0.887
4.894 0.9262 0.927 0.922 0.81 0.925 0.932 0.93 0.947 0.944 0.731 0.962 0.915 0.912
6.282 0.9733 0.958 0.945 0.835 0.955 0.966 0.964 0.979 0.967 0.757 0.994 0.949 0.945
SSE SSE 5.057e-04 1.688e-03 5.115e-02 7.144e-04 9.107e-05 1.128e-04 1.957e-03 3.884e-03 1.547e-01 5.725e-03 1.354e-03 1.316e-03
Table 6.1: 2c - Movement duration by utility model for experiment 2c.
eff_mass Movement Duration (s) Utility 1 Gross Duration Utility 2 Gross Duration Utility 3 Gross Duration Utility 1 Net Duration Utility 2 Net Duration Utility 3 Net Duration Utility Comb 1 Gross Duration Utility Comb 2 Gross Duration Utility Comb 3 Gross Duration Utility Comb 1 Net Duration Utility Comb 2 Net Duration Utility Comb 3 Net Duration
alpha alpha 75.113 99999.997 -23.62 94.012 99999.997 47.789 60.678 166.74 3.149 93.503 -7.803 20.122
2.506 0.6673 0.691 0.663 0.703 0.692 0.856 0.686 0.719 0.663 0.658 0.693 0.856 0.765
3.959 0.7429 0.746 0.707 0.745 0.748 0.913 0.746 0.776 0.707 0.703 0.749 0.913 0.825
4.894 0.7816 0.773 0.729 0.766 0.776 0.941 0.774 0.804 0.729 0.725 0.777 0.941 0.854
6.282 0.8234 0.807 0.756 0.79 0.811 0.974 0.811 0.839 0.756 0.751 0.812 0.974 0.89
SSE SSE 1.031e-01 1.039e-01 1.280e-02 1.029e-01 1.008e-01 1.004e-01 4.514e-03 8.613e-03 1.012e-02 8.479e-04 1.126e-01 2.597e-02
SSE Alternative utility models for 2a, 2b, and 2c.

Figure 6.1: SSE Alternative utility models for 2a, 2b, and 2c.

SSE Alternative utility models for 2a, 2b, and 2c.

Figure 6.2: SSE Alternative utility models for 2a, 2b, and 2c.

6.1.2 Two Alpha value

Table 6.2: 2a - Movement duration by utility model for experiment 2a.
eff_mass Movement Duration (s) Utility 1 Gross Duration Utility 2 Gross Duration Utility 3 Gross Duration Utility 1 Net Duration Utility 2 Net Duration Utility 3 Net Duration Utility Comb 1 Gross Duration Utility Comb 2 Gross Duration Utility Comb 3 Gross Duration Utility Comb 1 Net Duration Utility Comb 2 Net Duration Utility Comb 3 Net Duration
alpha alpha 54.463 259.211 -94.223 79.409 -59.453 21.098 60.678 166.74 3.149 93.503 -7.803 20.122
2.506 0.7807 0.785 0.804 0.809 0.785 0.777 0.785 0.774 0.76 0.66 0.764 0.846 0.788
3.959 0.8441 0.84 0.84 0.841 0.84 0.841 0.842 0.828 0.799 0.705 0.816 0.904 0.844
4.894 0.8677 0.868 0.86 0.857 0.868 0.871 0.87 0.855 0.819 0.727 0.843 0.932 0.872
6.282 0.9045 0.903 0.886 0.875 0.903 0.906 0.904 0.89 0.846 0.753 0.877 0.966 0.907
SSE SSE 3.832e-05 9.622e-04 1.796e-03 3.832e-05 3.679e-05 2.916e-05 6.750e-04 8.253e-03 7.665e-02 2.433e-03 1.578e-02 7.907e-05
Table 6.2: 2b - Movement duration by utility model for experiment 2b.
eff_mass Movement Duration (s) Utility 1 Gross Duration Utility 2 Gross Duration Utility 3 Gross Duration Utility 1 Net Duration Utility 2 Net Duration Utility 3 Net Duration Utility Comb 1 Gross Duration Utility Comb 2 Gross Duration Utility Comb 3 Gross Duration Utility Comb 1 Net Duration Utility Comb 2 Net Duration Utility Comb 3 Net Duration
alpha alpha 80.264 142.685 982.678 141.248 -2.762 5.921 60.678 166.74 3.149 93.503 -7.803 20.122
2.506 0.8457 0.862 0.875 0.764 0.865 0.846 0.849 0.878 0.899 0.665 0.897 0.826 0.836
3.959 0.9018 0.904 0.905 0.793 0.904 0.904 0.903 0.923 0.928 0.709 0.939 0.886 0.887
4.894 0.9262 0.927 0.922 0.81 0.925 0.932 0.93 0.947 0.944 0.731 0.962 0.915 0.912
6.282 0.9733 0.958 0.945 0.835 0.955 0.966 0.964 0.979 0.967 0.757 0.994 0.949 0.945
SSE SSE 5.057e-04 1.688e-03 5.115e-02 7.144e-04 9.107e-05 1.128e-04 1.957e-03 3.884e-03 1.547e-01 5.725e-03 1.354e-03 1.316e-03
Table 6.2: 2c - Movement duration by utility model for experiment 2c.
eff_mass Movement Duration (s) Utility 1 Gross Duration Utility 2 Gross Duration Utility 3 Gross Duration Utility 1 Net Duration Utility 2 Net Duration Utility 3 Net Duration Utility Comb 1 Gross Duration Utility Comb 2 Gross Duration Utility Comb 3 Gross Duration Utility Comb 1 Net Duration Utility Comb 2 Net Duration Utility Comb 3 Net Duration
alpha alpha 75.113 99999.997 -23.62 94.012 99999.997 47.789 75.113 99999.997 -23.62 94.012 99999.997 47.789
2.506 0.6673 0.691 0.663 0.703 0.692 0.856 0.686 0.691 0.663 0.703 0.692 0.856 0.686
3.959 0.7429 0.746 0.707 0.745 0.748 0.913 0.746 0.746 0.707 0.745 0.748 0.913 0.746
4.894 0.7816 0.773 0.729 0.766 0.776 0.941 0.774 0.773 0.729 0.766 0.776 0.941 0.774
6.282 0.8234 0.807 0.756 0.79 0.811 0.974 0.811 0.807 0.756 0.79 0.811 0.974 0.811
SSE SSE 1.031e-01 1.039e-01 1.280e-02 1.029e-01 1.008e-01 1.004e-01 9.131e-04 8.613e-03 2.636e-03 8.203e-04 1.126e-01 5.700e-04
SSE Alternative utility models for 2a, 2b, and 2c.

Figure 6.3: SSE Alternative utility models for 2a, 2b, and 2c.

SSE Alternative utility models for 2a, 2b, and 2c.

Figure 6.4: SSE Alternative utility models for 2a, 2b, and 2c.

6.2 Specific alternative models

6.2.1 One alpha value

This next plot/section is showing the total SSE when fitting one alpha to 2a/2b, then applied to 2c.

Table 6.3: Movement duration and predictions for experiment 2a. This is fitting one alpha value to experiment 2a/2b, then applying it to 2c.
Experimental Utility Gross Utility Net Utility Torque Net Reward Effeciency Gross Cost Net Cost
2.506 0.7807 0.7740 0.7640 0.6030 0.7600 0.7230 0.6627 0.8561
3.959 0.8441 0.8280 0.8160 0.7500 0.7990 0.7680 0.7074 0.9130
4.894 0.8677 0.8550 0.8430 0.8330 0.8190 0.7900 0.7291 0.9407
6.282 0.9045 0.8900 0.8770 0.9450 0.8460 0.8190 0.7556 0.9743
SSE 0.0000 0.0007 0.0024 0.0433 0.0083 0.0225 0.0740 0.0206
Table 6.3: Movement duration and predictions for experiment 2b. This is fitting one alpha value to experiment 2a/2b, then applying it to 2c.
Experimental 2b Utility Gross Utility Net Utility Torque Net Reward Effeciency Gross Cost Net Cost
2.506 0.8457 0.878 0.8970 0.6570 0.8990 0.844 0.6627 0.8561
3.959 0.9018 0.923 0.9390 0.7940 0.9280 0.881 0.7074 0.9130
4.894 0.9262 0.947 0.9620 0.8680 0.9440 0.901 0.7291 0.9407
6.282 0.9733 0.979 0.9940 0.9650 0.9670 0.929 0.7556 0.9743
SSE 0.0000 0.002 0.0057 0.0507 0.0039 0.003 0.1575 0.0004
Table 6.3: Movement duration and predictions for experiment 2c. This is fitting one alpha value to experiment 2a/2b, then applying it to 2c.
Experimental 2c Utility Gross Utility Net Utility Torque Net Reward Effeciency Gross Cost Net Cost
2.506 0.6673 0.7190 0.6930 0.5530 0.6630 0.6630 0.6627 0.8561
3.959 0.7429 0.7760 0.7490 0.7100 0.7070 0.7070 0.7074 0.9130
4.894 0.7816 0.8040 0.7770 0.7970 0.7290 0.7290 0.7291 0.9407
6.282 0.8234 0.8390 0.8120 0.9110 0.7560 0.7560 0.7556 0.9743
SSE 0.0000 0.0045 0.0008 0.0221 0.0086 0.0086 0.0086 0.1127

6.2.2 Plotting specific models

Table 6.4: SSE of Specific utility models. Fitted 1 alpha.
exp utnum utmod sse
2a 1 Utility Gross 0.0006750
2a 2 Utility Net 0.0024330
2a 3 Utility Torque 0.0432700
2a 4 Net Reward 0.0082530
2a 5 Effeciency 0.0224600
2a 6 Gross Cost 0.0739800
2a 7 Net Cost 0.0206400
2b 1 Utility Gross 0.0019570
2b 2 Utility Net 0.0057250
2b 3 Utility Torque 0.0506800
2b 4 Net Reward 0.0038840
2b 5 Effeciency 0.0030350
2b 6 Gross Cost 0.1575000
2b 7 Net Cost 0.0004426
2c 1 Utility Gross 0.0045140
2c 2 Utility Net 0.0008479
2c 3 Utility Torque 0.0220600
2c 4 Net Reward 0.0086130
2c 5 Effeciency 0.0086130
2c 6 Gross Cost 0.0086350
2c 7 Net Cost 0.1127000
Table 6.4: SSE of Specific utility models. Fitted 1 alpha.
utmod sse
Effeciency 0.0341080
Gross Cost 0.2401150
Net Cost 0.1337826
Net Reward 0.0207500
Utility Gross 0.0071460
Utility Net 0.0090059
Utility Torque 0.1160100

6.3 SSE NORMALIZED

Table 6.5: SSE NORM of Specific utility models. Fitted 1 alpha.
exp utnum utmod sse
2a 1 Utility Gross 0.0002558
2a 2 Utility Net 0.0003548
2a 4 Net Reward 0.0041090
2a 6 Gross Cost 0.0006631
2a 7 Net Cost 0.0007998
2a 3 Utility Torque 0.2662000
2a 5 Efficiency 0.0005844
2b 1 Utility Gross 0.0017960
2b 2 Utility Net 0.0027340
2b 4 Net Reward 0.0088790
2b 6 Gross Cost 0.0001424
2b 7 Net Cost 0.0001762
2b 3 Utility Torque 0.1723000
2b 5 Efficiency 0.0007889
2c 1 Utility Gross 0.0084520
2c 2 Utility Net 0.0074190
2c 4 Net Reward 0.0161000
2c 6 Gross Cost 0.0159500
2c 7 Net Cost 0.0166100
2c 3 Utility Torque 0.2730000
2c 5 Efficiency 0.0161000
Table 6.5: SSE NORM of Specific utility models. Fitted 1 alpha.
utmod sse
Efficiency 0.0174733
Gross Cost 0.0167555
Net Cost 0.0175860
Net Reward 0.0290880
Utility Gross 0.0105038
Utility Net 0.0105078
Utility Torque 0.7115000

7 Making the utility plot

8 Cross-Validation Tables

8.1 Fit to 2a, predicting 2a, 2b, 2c

Table 8.1: Fitted one alpha to 2a, predicting 2a.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 54.463 79.409 1.311
2.506 0.7807 0.785 0.785 0.617 0.804 0.723 0.6627 0.8561
3.959 0.8441 0.84 0.84 0.777 0.84 0.768 0.7074 0.913
4.894 0.8677 0.868 0.868 0.867 0.86 0.79 0.7291 0.9407
6.282 0.9045 0.903 0.903 0.989 0.886 0.819 0.7556 0.9743
SSE 3.832e-05 3.832e-05 3.844e-02 9.622e-04 2.246e-02 7.398e-02 2.064e-02
AIC -42.2236 -42.2236 -14.5802 -29.3303 -16.7291 -11.9609 -17.0676
BIC -43.451 -43.451 -15.8076 -30.5577 -17.9565 -13.1883 -18.295
Table 8.2: Fitted one alpha to 2a, predicting 2b.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 54.463 79.409 1.311
2.506 0.8457 0.785 0.785 0.617 0.804 0.723 0.6627 0.8561
3.959 0.9018 0.84 0.84 0.777 0.84 0.768 0.7074 0.913
4.894 0.9262 0.868 0.868 0.867 0.86 0.79 0.7291 0.9407
6.282 0.9733 0.903 0.903 0.989 0.886 0.819 0.7556 0.9743
SSE 1.584e-02 1.584e-02 7.163e-02 1.757e-02 7.532e-02 1.575e-01 4.426e-04
AIC -18.1272 -18.1272 -12.0902 -17.7124 -11.8891 -8.9376 -32.4363
BIC -19.3546 -19.3546 -13.3177 -18.9398 -13.1165 -10.165 -33.6637
Table 8.3: Fitted one alpha to 2a, predicting 2c.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 54.463 79.409 1.311
2.506 0.6673 0.785 0.785 0.617 0.804 0.723 0.6627 0.8561
3.959 0.7429 0.84 0.84 0.777 0.84 0.768 0.7074 0.913
4.894 0.7816 0.868 0.868 0.867 0.86 0.79 0.7291 0.9407
6.282 0.8234 0.903 0.903 0.989 0.886 0.819 0.7556 0.9743
SSE 3.709e-02 3.709e-02 3.842e-02 3.818e-02 3.822e-03 8.635e-03 1.127e-01
AIC -14.7232 -14.7232 -14.5821 -14.6066 -23.8133 -20.553 -10.2786
BIC -15.9506 -15.9506 -15.8095 -15.834 -25.0407 -21.7804 -11.506

8.2 Fit to 2b, predicting 2a, 2b, 2c

Table 8.4: Fitted one alpha to 2b, predicting 2a.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 80.264 141.248 28.046
2.506 0.7807 0.862 0.865 0.75 0.875 0.844 0.6627 0.8561
3.959 0.8441 0.904 0.904 0.803 0.905 0.881 0.7074 0.913
4.894 0.8677 0.927 0.925 0.838 0.922 0.901 0.7291 0.9407
6.282 0.9045 0.958 0.955 0.889 0.945 0.929 0.7556 0.9743
SSE 1.658e-02 1.654e-02 3.752e-03 1.720e-02 7.083e-03 7.398e-02 2.064e-02
AIC -17.9424 -17.9541 -23.887 -17.797 -21.3454 -11.9609 -17.0676
BIC -19.1698 -19.1815 -25.1144 -19.0244 -22.5728 -13.1883 -18.295
Table 8.5: Fitted one alpha to 2b, predicting 2b.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 80.264 141.248 28.046
2.506 0.8457 0.862 0.865 0.75 0.875 0.844 0.6627 0.8561
3.959 0.9018 0.904 0.904 0.803 0.905 0.881 0.7074 0.913
4.894 0.9262 0.927 0.925 0.838 0.922 0.901 0.7291 0.9407
6.282 0.9733 0.958 0.955 0.889 0.945 0.929 0.7556 0.9743
SSE 5.057e-04 7.144e-04 3.381e-02 1.688e-03 3.035e-03 1.575e-01 4.426e-04
AIC -31.9033 -30.5216 -15.0932 -27.0808 -24.7355 -8.9376 -32.4363
BIC -33.1307 -31.749 -16.3206 -28.3083 -25.9629 -10.165 -33.6637
Table 8.6: Fitted one alpha to 2b, predicting 2c.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 80.264 141.248 28.046
2.506 0.6673 0.862 0.865 0.75 0.875 0.844 0.6627 0.8561
3.959 0.7429 0.904 0.904 0.803 0.905 0.881 0.7074 0.913
4.894 0.7816 0.927 0.925 0.838 0.922 0.901 0.7291 0.9407
6.282 0.8234 0.958 0.955 0.889 0.945 0.929 0.7556 0.9743
SSE 1.031e-01 1.029e-01 1.794e-02 1.039e-01 7.571e-02 8.635e-03 1.127e-01
AIC -10.6324 -10.6401 -17.6285 -10.6017 -11.8687 -20.553 -10.2786
BIC -11.8598 -11.8675 -18.8559 -11.8291 -13.0961 -21.7804 -11.506

8.3 Fit to 2c, predicting 2a, 2b, 2c

Table 8.7: Fitted one alpha to 2c, predicting 2a.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 75.113 94.012 25.188
2.506 0.7807 0.691 0.692 0.529 0.663 0.663 0.6627 0.8561
3.959 0.8441 0.746 0.748 0.694 0.707 0.707 0.7074 0.913
4.894 0.8677 0.773 0.776 0.785 0.729 0.729 0.7291 0.9407
6.282 0.9045 0.807 0.811 0.927 0.756 0.756 0.7556 0.9743
SSE 3.613e-02 3.424e-02 9.322e-02 7.393e-02 7.393e-02 7.398e-02 2.064e-02
AIC -14.8272 -15.0421 -11.0366 -11.9639 -11.9639 -11.9609 -17.0676
BIC -16.0546 -16.2695 -12.264 -13.1913 -13.1913 -13.1883 -18.295
Table 8.8: Fitted one alpha to 2c, predicting 2b.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 75.113 94.012 25.188
2.506 0.8457 0.691 0.692 0.529 0.663 0.663 0.6627 0.8561
3.959 0.9018 0.746 0.748 0.694 0.707 0.707 0.7074 0.913
4.894 0.9262 0.773 0.776 0.785 0.729 0.729 0.7291 0.9407
6.282 0.9733 0.807 0.811 0.927 0.756 0.756 0.7556 0.9743
SSE 9.934e-02 9.619e-02 1.656e-01 1.574e-01 1.574e-01 1.575e-01 4.426e-04
AIC -10.7821 -10.9111 -8.7388 -8.94 -8.94 -8.9376 -32.4363
BIC -12.0095 -12.1385 -9.9662 -10.1674 -10.1674 -10.165 -33.6637
Table 8.9: Fitted one alpha to 2c, predicting 2c.
Experimental Mvttimes Utility Grs Utility Net Utility Torque Net Rwd Grs Efficiency Gross Cost Net Cost
alpha 75.113 94.012 25.188
2.506 0.6673 0.691 0.692 0.529 0.663 0.663 0.6627 0.8561
3.959 0.7429 0.746 0.748 0.694 0.707 0.707 0.7074 0.913
4.894 0.7816 0.773 0.776 0.785 0.729 0.729 0.7291 0.9407
6.282 0.8234 0.807 0.811 0.927 0.756 0.756 0.7556 0.9743
SSE 9.131e-04 8.203e-04 3.227e-02 8.613e-03 8.613e-03 8.635e-03 1.127e-01
AIC -29.5398 -29.9686 -15.2799 -20.5631 -20.5631 -20.553 -10.2786
BIC -30.7672 -31.196 -16.5074 -21.7905 -21.7905 -21.7804 -11.506

9 2a Durations

9.1 Model Plotting Function

9.2 DF Creation

9.3 Peak Velocity Plotting

9.4 SSE of models - Exp 2a

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure ??.

9.4.1 Absolute

This table shows the SSE for the 2a movement duration and peak velocity predictions.

Table 9.1: Exp 2a - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 2.164e-03 -2.81e+01 -2.87e+01 1.130e-03 -3.07e+01 -3.13e+01
SSE.3 Met Cost Gross 7.398e-02 -1.40e+01 -1.46e+01 4.167e-03 -2.55e+01 -2.61e+01
SSE.4 Met Cost Net 2.064e-02 -1.91e+01 -1.97e+01 3.337e-03 -2.64e+01 -2.70e+01
SSE.5 Torque^2 3.844e-02 -1.66e+01 -1.72e+01 2.439e-03 -2.76e+01 -2.82e+01
SSE.7 Utility Gross 3.832e-05 -4.22e+01 -4.35e+01 6.140e-04 -3.11e+01 -3.24e+01
SSE.9 Utility Net 3.832e-05 -4.22e+01 -4.35e+01 6.140e-04 -3.11e+01 -3.24e+01
SSE.10 Utility Gross Combined Alpha 6.750e-04 -3.07e+01 -3.20e+01 3.872e-04 -3.30e+01 -3.42e+01
SSE.11 Utility Net Combined Alpha 2.433e-03 -2.56e+01 -2.68e+01 2.514e-04 -3.47e+01 -3.59e+01

9.4.2 Normalized

Table 9.2: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 1.386e-02 -2.07e+01 -2.13e+01 3.207e-02 -1.73e+01 -1.79e+01
SSE.3 Met Cost Gross 6.631e-04 -3.28e+01 -3.34e+01 1.014e-02 -2.19e+01 -2.25e+01
SSE.4 Met Cost Net 7.998e-04 -3.21e+01 -3.27e+01 1.056e-02 -2.17e+01 -2.24e+01
SSE.5 Torque^2 3.154e-01 -8.16e+00 -8.77e+00 6.310e-02 -1.46e+01 -1.52e+01
SSE.7 Utility Gross 2.279e-04 -3.51e+01 -3.63e+01 8.426e-03 -2.07e+01 -2.19e+01
SSE.9 Utility Net 2.279e-04 -3.51e+01 -3.63e+01 8.426e-03 -2.07e+01 -2.19e+01
SSE.10 Utility Gross Combined Alpha 2.558e-04 -3.46e+01 -3.59e+01 8.582e-03 -2.06e+01 -2.18e+01
SSE.11 Utility Net Combined Alpha 3.548e-04 -3.33e+01 -3.45e+01 9.014e-03 -2.04e+01 -2.16e+01

9.5 2a Modeling Plot

Modeling Results

Figure 9.1: Modeling Results

10 2b Durations

10.1 DF Creation

10.2 Peak Velocity Plotting

10.3 SSE of models - Exp 2b

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure ??.

10.3.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions.

Table 10.1: Exp 2b - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 1.753e-02 -1.97e+01 -2.03e+01 1.510e-03 -2.95e+01 -3.01e+01
SSE.3 Met Cost Gross 1.575e-01 -1.09e+01 -1.16e+01 1.411e-02 -2.06e+01 -2.12e+01
SSE.4 Met Cost Net 4.426e-04 -3.44e+01 -3.51e+01 1.442e-04 -3.89e+01 -3.95e+01
SSE.5 Torque^2 7.163e-02 -1.41e+01 -1.47e+01 7.450e-03 -2.31e+01 -2.38e+01
SSE.7 Utility Gross 5.057e-04 -3.19e+01 -3.31e+01 2.504e-04 -3.47e+01 -3.59e+01
SSE.9 Utility Net 7.144e-04 -3.05e+01 -3.17e+01 2.837e-04 -3.42e+01 -3.54e+01
SSE.10 Utility Gross Combined Alpha 2.260e-02 -1.67e+01 -1.79e+01 1.776e-03 -2.69e+01 -2.81e+01
SSE.11 Utility Net Combined Alpha 3.024e-02 -1.55e+01 -1.68e+01 2.342e-03 -2.58e+01 -2.70e+01

10.3.2 Normalized

Table 10.2: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 9.491e-03 -2.22e+01 -2.28e+01 2.533e-02 -1.82e+01 -1.89e+01
SSE.3 Met Cost Gross 1.424e-04 -3.90e+01 -3.96e+01 6.723e-03 -2.36e+01 -2.42e+01
SSE.4 Met Cost Net 1.762e-04 -3.81e+01 -3.87e+01 7.060e-03 -2.34e+01 -2.40e+01
SSE.5 Torque^2 3.376e-01 -7.89e+00 -8.50e+00 7.378e-02 -1.40e+01 -1.46e+01
SSE.7 Utility Gross 2.272e-03 -2.59e+01 -2.71e+01 1.346e-02 -1.88e+01 -2.00e+01
SSE.9 Utility Net 3.323e-03 -2.44e+01 -2.56e+01 1.550e-02 -1.82e+01 -1.94e+01
SSE.10 Utility Gross Combined Alpha 1.001e-04 -3.84e+01 -3.96e+01 5.406e-03 -2.24e+01 -2.37e+01
SSE.11 Utility Net Combined Alpha 7.777e-05 -3.94e+01 -4.06e+01 5.738e-03 -2.22e+01 -2.34e+01

10.4 2b Modeling Plot

Modeling Results

Figure 10.1: Modeling Results

11 2c Durations

11.1 DF Creation

11.2 Peak Velocity Plotting

11.3 SSE of models - Exp 2c

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiment at the same time. This alpha value is used to make figure ??.

11.3.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions.

Table 11.1: Exp 2b - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.208e-02 -1.62e+01 -1.68e+01 6.517e-02 -1.45e+01 -1.51e+01
SSE.3 Met Cost Gross 8.635e-03 -2.26e+01 -2.32e+01 2.855e-02 -1.78e+01 -1.84e+01
SSE.4 Met Cost Net 1.127e-01 -1.23e+01 -1.29e+01 8.239e-02 -1.35e+01 -1.41e+01
SSE.5 Torque^2 3.842e-02 -1.66e+01 -1.72e+01 4.795e-02 -1.57e+01 -1.63e+01
SSE.7 Utility Gross 9.131e-04 -2.95e+01 -3.08e+01 3.840e-02 -1.46e+01 -1.58e+01
SSE.9 Utility Net 8.203e-04 -3.00e+01 -3.12e+01 3.898e-02 -1.45e+01 -1.58e+01
SSE.10 Utility Gross Combined Alpha 2.845e-02 -1.58e+01 -1.70e+01 6.036e-02 -1.28e+01 -1.40e+01
SSE.11 Utility Net Combined Alpha 2.134e-02 -1.69e+01 -1.82e+01 5.730e-02 -1.30e+01 -1.42e+01

11.3.2 Normalized

Table 11.2: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.774e-02 -1.57e+01 -1.63e+01 3.463e-02 -1.70e+01 -1.76e+01
SSE.3 Met Cost Gross 1.595e-02 -2.01e+01 -2.07e+01 1.165e-02 -2.14e+01 -2.20e+01
SSE.4 Met Cost Net 1.661e-02 -1.99e+01 -2.06e+01 1.210e-02 -2.12e+01 -2.18e+01
SSE.5 Torque^2 2.123e-01 -9.75e+00 -1.04e+01 5.985e-02 -1.48e+01 -1.54e+01
SSE.7 Utility Gross 8.253e-03 -2.07e+01 -2.20e+01 6.489e-03 -2.17e+01 -2.29e+01
SSE.9 Utility Net 7.363e-03 -2.12e+01 -2.24e+01 5.906e-03 -2.21e+01 -2.33e+01
SSE.10 Utility Gross Combined Alpha 1.338e-02 -1.88e+01 -2.00e+01 9.972e-03 -2.00e+01 -2.12e+01
SSE.11 Utility Net Combined Alpha 1.404e-02 -1.86e+01 -1.98e+01 1.044e-02 -1.98e+01 -2.10e+01

11.4 2c Modeling Plot

Modeling Results

Figure 11.1: Modeling Results